Plots:

Summary plots - For the summary plots, each plot is paired by parameter level vertically and the values in the cells are the mean value across all of the simulations for that parameter level. Sample strategy is on the y-axis and number of sites is on the x-axis.Note that each average encompasses all of the other varying simulation parameters.

Full plots - For the full plots, Each plot represents a unique simulation and the values in the cells are the mean value across all of the 10 iterations of that simulation across all three unique landscape seeds (i.e., all three sets of Neutral Landscape Models) for a total of 30 replicates. Sample strategy is on the y-axis and number of sites is on the x-axis. Since there are a many simulations presented in the full plots, here is a handy key for how the different parameters are laid out within them (H = High, L = Low):

Methods:

K - number of latent factors used in LFMM

TPR - True Positive Rate

FDR - False Discovery Rate

strict vs relaxed TPR/FDR - “relaxed” means any adaptive loci identified was counted as a true positive and “strict” means only an adaptive loci identified with the correct environmental variable was counted as a true positive

pRDA - partial RDA conditioning on two PC axes to control for population genetic structure

lasso vs ridge- “lasso” and “ridge” are different methods utilized by LFMM that have different penalization functions (Caye et al., 2019)

1. LFMM

1.1 Individual sampling

1.1.1 Summary plots

1.1.2 Linear mixed effects models

Only results from the ridge method are used from here on out

Linear mixed effect model
TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0008 53.2028 53.2028 1 15.3480K 1263.83866 4.4 × 10−266*
Population size 0.0763 22.3781 22.3781 1 15.3480K 531.59489 1.2 × 10−115*
Migration 0.2604 260.3385 260.3385 1 15.3480K 6184.36896 0.0*
Selection strength 0.0256 2.5157 2.5157 1 15.3480K 59.76088 1.1 × 10−14*
Spatial autocorrelation 0.3835 564.7879 564.7879 1 15.3480K 13416.59552 0.0*
Environmental correlation −0.0546 11.4612 11.4612 1 15.3480K 272.26221 1.2 × 10−60*
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G −0.0009 0.0047 −0.2029 0.99704719 1.0e+00
ES - R 0.0114 0.0047 2.4382 0.07008603 7.0e-02
ES - T 0.0513 0.0047 10.9528 3.8 × 10−14 3.8e-14
G - R 0.0124 0.0047 2.6410 0.04118167 4.1e-02
G - T 0.0522 0.0047 11.1557 1.2 × 10−14 1.2e-14
R - T 0.0399 0.0047 8.5146 3.7 × 10−14 3.7e-14
Linear mixed effect model
TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0008 53.5184 53.5184 1 15.3480K 1289.21597 3.6 × 10−271*
Population size 0.0732 20.5782 20.5782 1 15.3480K 495.71192 4.2 × 10−108*
Migration 0.2591 257.7774 257.7774 1 15.3480K 6209.65003 0.0*
Selection strength 0.0242 2.2525 2.2525 1 15.3480K 54.26063 1.8 × 10−13*
Spatial autocorrelation 0.3761 543.2885 543.2885 1 15.3480K 13087.38352 0.0*
Environmental correlation −0.0567 12.3237 12.3237 1 15.3480K 296.86851 6.6 × 10−66*
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G −0.0020 0.0046 −0.4350 0.97243790 9.7e-01
ES - R 0.0108 0.0046 2.3148 0.09463102 9.5e-02
ES - T 0.0522 0.0046 11.2193 8.9 × 10−15 8.9e-15
G - R 0.0128 0.0046 2.7499 0.03037337 3.0e-02
G - T 0.0542 0.0046 11.6543 0.0 0.0e+00
R - T 0.0414 0.0046 8.9045 2.8 × 10−14 2.8e-14
Linear mixed effect model
FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0026 505.5285 505.5285 1 15.3480K 4.033406e+03 0.0*
Population size 0.0070 0.1878 0.1878 1 15.3480K 1.498216e+00 0.22
Migration −0.0004 0.0006 0.0006 1 15.3480K 4.999228e-03 0.94
Selection strength −0.0199 1.5277 1.5277 1 15.3480K 1.218901e+01 4.8 × 10−4*
Spatial autocorrelation 0.0552 11.7204 11.7204 1 15.3480K 9.351249e+01 4.7 × 10−22*
Environmental correlation 0.0308 3.6511 3.6511 1 15.3480K 2.913101e+01 6.9 × 10−8*
* p < 0.001
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G 0.0168 0.0081 2.0818 0.1590172 1.6e-01
ES - R 0.0130 0.0081 1.6075 0.3742953 3.7e-01
ES - T −0.0272 0.0081 −3.3699 4.2 × 10−3 4.2e-03
G - R −0.0038 0.0081 −0.4743 0.9647549 9.6e-01
G - T −0.0440 0.0081 −5.4517 3.0 × 10−7 3.0e-07
R - T −0.0402 0.0081 −4.9774 3.8 × 10−6 3.8e-06
Linear mixed effect model
FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0025 492.6077 492.6077 1 15.3480K 3893.485885 0.0*
Population size 0.0164 1.0308 1.0308 1 15.3480K 8.147285 4.3 × 10−3**
Migration 0.0027 0.0270 0.0270 1 15.3480K 0.213428 0.6400
Selection strength −0.0149 0.8485 0.8485 1 15.3480K 6.706348 0.0096**
Spatial autocorrelation 0.0734 20.6903 20.6903 1 15.3480K 163.532211 3.0 × 10−37*
Environmental correlation 0.0363 5.0474 5.0474 1 15.3480K 39.893688 2.8 × 10−10*
* p < 0.001
** p < 0.01
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G 0.0191 0.0081 2.3496 0.08711056 8.7e-02
ES - R 0.0144 0.0081 1.7719 0.28690133 2.9e-01
ES - T −0.0285 0.0081 −3.5108 2.5 × 10−3 2.5e-03
G - R −0.0047 0.0081 −0.5776 0.93881608 9.4e-01
G - T −0.0476 0.0081 −5.8604 2.8 × 10−8 2.8e-08
R - T −0.0429 0.0081 −5.2827 7.6 × 10−7 7.6e-07

1.1.3 Full plots

1.2 Site sampling

1.2.1 Summary plots

1.1.2 Linear mixed effects models

Only results from the ridge method are used from here on out

Linear mixed effect model
TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0029 3.2042 3.2042 1 8.6290K 140.5760485 3.5 × 10−32*
Population size 0.0308 2.0477 2.0477 1 8.6290K 89.8352521 3.3 × 10−21*
Migration 0.0787 13.3647 13.3647 1 8.6290K 586.3375067 2.2 × 10−125*
Selection strength −0.0015 0.0047 0.0047 1 8.6290K 0.2052864 0.65
Spatial autocorrelation 0.1968 83.6960 83.6960 1 8.6290K 3671.9104037 0.0*
Environmental correlation −0.0566 6.9313 6.9313 1 8.6290K 304.0919069 5.9 × 10−67*
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES −0.0269 0.0040 −6.7676 3.9 × 10−11 3.9e-11
EQ - R −0.0074 0.0040 −1.8703 0.147366 1.5e-01
ES - R 0.0195 0.0040 4.8974 2.9 × 10−6 2.9e-06
Linear mixed effect model
TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0020 1.4302 1.4302 1 8.6290K 67.970410 1.9 × 10−16*
Population size 0.0284 1.7480 1.7480 1 8.6290K 83.077065 9.7 × 10−20*
Migration 0.0868 16.2650 16.2650 1 8.6290K 773.013161 5.2 × 10−163*
Selection strength −0.0034 0.0245 0.0245 1 8.6290K 1.163182 0.28
Spatial autocorrelation 0.1897 77.7389 77.7389 1 8.6290K 3694.635667 0.0*
Environmental correlation −0.0562 6.8328 6.8328 1 8.6290K 324.738752 2.7 × 10−71*
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES −0.0234 0.0038 −6.1133 2.9 × 10−9 2.9e-09
EQ - R −0.0046 0.0038 −1.1935 0.4570187 4.6e-01
ES - R 0.0188 0.0038 4.9198 2.6 × 10−6 2.6e-06
Linear mixed effect model
FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0178 117.4584 117.4584 1 8.6290K 2365.005677 0.0*
Population size 0.0054 0.0639 0.0639 1 8.6290K 1.285793 0.26
Migration −0.0658 9.3587 9.3587 1 8.6290K 188.434971 1.9 × 10−42*
Selection strength −0.0066 0.0953 0.0953 1 8.6290K 1.918980 0.17
Spatial autocorrelation −0.0233 1.1748 1.1748 1 8.6290K 23.654165 1.2 × 10−6*
Environmental correlation 0.0062 0.0820 0.0820 1 8.6290K 1.651659 0.20
* p < 0.001
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES −0.0424 0.0059 −7.2249 1.5 × 10−12 1.5e-12
EQ - R −0.0509 0.0059 −8.6624 2.5 × 10−14 2.5e-14
ES - R −0.0084 0.0059 −1.4376 0.3215746 3.2e-01
Linear mixed effect model
FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0177 115.9461 115.9461 1 8.6290K 2333.109893 0.0*
Population size 0.0063 0.0856 0.0856 1 8.6290K 1.723408 0.19
Migration −0.0650 9.1374 9.1374 1 8.6290K 183.866796 1.8 × 10−41*
Selection strength −0.0065 0.0927 0.0927 1 8.6290K 1.864595 0.17
Spatial autocorrelation −0.0205 0.9050 0.9050 1 8.6290K 18.210895 2.0 × 10−5*
Environmental correlation 0.0069 0.1024 0.1024 1 8.6290K 2.061300 0.15
* p < 0.001
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES −0.0433 0.0059 −7.3719 5.2 × 10−13 5.2e-13
EQ - R −0.0507 0.0059 −8.6318 2.6 × 10−14 2.6e-14
ES - R −0.0074 0.0059 −1.2599 0.4179973 4.2e-01

1.2.3 Full plots

2. RDA

2.1 Individual sampling

2.1.1 Summary plots

2.1.2 Linear mixed effects models

Only results from the standard RDA (not the partial RDA) are used from here on out

Linear mixed effect model
TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0007 37.4207 37.4207 1 15.3480K 860.515512 4.3 × 10−184*
Population size 0.0374 5.3737 5.3737 1 15.3480K 123.571864 1.3 × 10−28*
Migration 0.2896 321.9753 321.9753 1 15.3480K 7404.049535 0.0*
Selection strength −0.0037 0.0516 0.0516 1 15.3480K 1.185546 0.28
Spatial autocorrelation 0.2868 315.8296 315.8296 1 15.3480K 7262.724755 0.0*
Environmental correlation 0.0169 1.0931 1.0931 1 15.3480K 25.136567 5.4 × 10−7*
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G −0.0004 0.0048 −0.0747 0.9998509 1.0e+00
ES - R 0.0089 0.0048 1.8779 0.2375584 2.4e-01
ES - T 0.0333 0.0048 6.9911 1.6 × 10−11 1.6e-11
G - R 0.0093 0.0048 1.9525 0.2062836 2.1e-01
G - T 0.0336 0.0048 7.0658 9.6 × 10−12 9.6e-12
R - T 0.0243 0.0048 5.1133 1.9 × 10−6 1.9e-06
Linear mixed effect model
TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0006 32.6703 32.6703 1 15.3480K 841.258694 4.0 × 10−180*
Population size 0.0340 4.4409 4.4409 1 15.3480K 114.352267 1.4 × 10−26*
Migration 0.2673 274.3571 274.3571 1 15.3480K 7064.686800 0.0*
Selection strength −0.0054 0.1111 0.1111 1 15.3480K 2.859800 0.091
Spatial autocorrelation 0.2643 268.3236 268.3236 1 15.3480K 6909.325831 0.0*
Environmental correlation 0.0036 0.0495 0.0495 1 15.3480K 1.274395 0.260
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G 0.0000 0.0045 −0.0090 0.9999997 1.0e+00
ES - R 0.0087 0.0045 1.9315 0.2147867 2.1e-01
ES - T 0.0342 0.0045 7.6014 2.0 × 10−13 2.0e-13
G - R 0.0087 0.0045 1.9405 0.2111304 2.1e-01
G - T 0.0342 0.0045 7.6104 1.9 × 10−13 1.9e-13
R - T 0.0255 0.0045 5.6699 8.6 × 10−8 8.6e-08
Linear mixed effect model
FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0002 3.7712 3.7712 1 15.3480K 80.61223 3.1 × 10−19*
Population size 0.0151 0.8807 0.8807 1 15.3480K 18.82572 1.4 × 10−5*
Migration 0.1369 71.9514 71.9514 1 15.3480K 1538.02432 1.1 × 10−320*
Selection strength −0.0121 0.5603 0.5603 1 15.3480K 11.97778 5.4 × 10−4*
Spatial autocorrelation −0.0490 9.2366 9.2366 1 15.3480K 197.43966 1.4 × 10−44*
Environmental correlation 0.0221 1.8688 1.8688 1 15.3480K 39.94790 2.7 × 10−10*
* p < 0.001
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G −0.0092 0.0049 −1.8701 0.2409603 0.24000
ES - R 0.0063 0.0049 1.2790 0.5763683 0.58000
ES - T 0.0094 0.0049 1.9034 0.2265099 0.23000
G - R 0.0155 0.0049 3.1491 8.9 × 10−3 0.00890
G - T 0.0186 0.0049 3.7736 9.3 × 10−4 0.00093
R - T 0.0031 0.0049 0.6245 0.9242557 0.92000
Linear mixed effect model
FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0003 4.9052 4.9052 1 15.3480K 96.998095 8.1 × 10−23*
Population size 0.0208 1.6581 1.6581 1 15.3480K 32.788661 1.0 × 10−8*
Migration 0.1636 102.8145 102.8145 1 15.3480K 2033.124890 0.0*
Selection strength −0.0083 0.2627 0.2627 1 15.3480K 5.194032 0.023**
Spatial autocorrelation −0.0199 1.5265 1.5265 1 15.3480K 30.186505 4.0 × 10−8*
Environmental correlation 0.0400 6.1469 6.1469 1 15.3480K 121.553432 3.7 × 10−28*
* p < 0.001
** p < 0.05
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
ES - G −0.0085 0.0051 −1.6486 0.3513345 0.3500
ES - R 0.0080 0.0051 1.5562 0.4039088 0.4000
ES - T 0.0089 0.0051 1.7350 0.3054615 0.3100
G - R 0.0164 0.0051 3.2048 7.4 × 10−3 0.0074
G - T 0.0174 0.0051 3.3835 4.0 × 10−3 0.0040
R - T 0.0009 0.0051 0.1787 0.9979738 1.0000

1.1.3 Full plots

2.2 Site sampling

2.2.1 Summary plots

2.2.2 Linear mixed effects models

Only results from the standard RDA (not the partial RDA) are used from here on out

Linear mixed effect model
TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0032 3.7382 3.7382 1 8.6290K 126.204793 4.4 × 10−29*
Population size −0.0256 1.4139 1.4139 1 8.6290K 47.732732 5.2 × 10−12*
Migration 0.3026 197.8044 197.8044 1 8.6290K 6677.977925 0.0*
Selection strength 0.0247 1.3192 1.3192 1 8.6290K 44.536716 2.7 × 10−11*
Spatial autocorrelation 0.2649 151.5702 151.5702 1 8.6290K 5117.088582 0.0*
Environmental correlation −0.0095 0.1964 0.1964 1 8.6290K 6.630773 0.01
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES −0.0076 0.0045 −1.6762 0.2143549 2.1e-01
EQ - R 0.0216 0.0045 4.7556 5.9 × 10−6 5.9e-06
ES - R 0.0292 0.0045 6.4317 3.8 × 10−10 3.8e-10
Linear mixed effect model
TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0035 4.5757 4.5757 1 8.6290K 179.59833 1.5 × 10−40*
Population size −0.0218 1.0312 1.0312 1 8.6290K 40.47586 2.1 × 10−10*
Migration 0.2649 151.6270 151.6270 1 8.6290K 5951.39931 0.0*
Selection strength 0.0171 0.6304 0.6304 1 8.6290K 24.74158 6.7 × 10−7*
Spatial autocorrelation 0.2326 116.8869 116.8869 1 8.6290K 4587.84166 0.0*
Environmental correlation −0.0218 1.0254 1.0254 1 8.6290K 40.24545 2.4 × 10−10*
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES −0.0071 0.0042 −1.6889 0.2094071 2.1e-01
EQ - R 0.0183 0.0042 4.3478 4.1 × 10−5 4.1e-05
ES - R 0.0254 0.0042 6.0367 4.7 × 10−9 4.7e-09
Linear mixed effect model
FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0031 3.6639 3.6639 1 8.6290K 56.113654 7.5 × 10−14*
Population size −0.3353 242.8022 242.8022 1 8.6290K 3718.564269 0.0*
Migration 0.6147 816.1570 816.1570 1 8.6290K 12499.609497 0.0*
Selection strength 0.0220 1.0484 1.0484 1 8.6290K 16.056600 6.2 × 10−5*
Spatial autocorrelation −0.0630 8.5651 8.5651 1 8.6290K 131.176414 3.7 × 10−30*
Environmental correlation 0.0143 0.4433 0.4433 1 8.6290K 6.788829 0.0092**
* p < 0.001
** p < 0.01
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES 0.0026 0.0067 0.3862 0.9210664 0.92
EQ - R 0.0100 0.0067 1.4820 0.2995710 0.30
ES - R 0.0074 0.0067 1.0957 0.5166979 0.52
Linear mixed effect model
FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0028 2.8102 2.8102 1 8.6290K 44.31433 3.0 × 10−11*
Population size −0.3134 212.1999 212.1999 1 8.6290K 3346.14362 0.0*
Migration 0.6419 890.0377 890.0377 1 8.6290K 14034.85129 0.0*
Selection strength 0.0267 1.5441 1.5441 1 8.6290K 24.34830 8.2 × 10−7*
Spatial autocorrelation −0.0410 3.6335 3.6335 1 8.6290K 57.29578 4.1 × 10−14*
Environmental correlation 0.0233 1.1743 1.1743 1 8.6290K 18.51783 1.7 × 10−5*
* p < 0.001
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p p
EQ - ES 0.0020 0.0066 0.3010 0.9512842 0.95
EQ - R 0.0120 0.0066 1.8016 0.1690281 0.17
ES - R 0.0100 0.0066 1.5006 0.2906260 0.29

2.2.3 Full plots

Figures: